Pre-Calc Exam Notes 19 - Applications and Solving Right...

Applications and Solving Right Triangles • Section 1.3 19 θ r cos θ r sin θ r For some problems it may help to remember that when a right tri-angle has a hypotenuse of length r and an acute angle θ , as in the picture on the right, the adjacent side will have length r cos θ and the opposite side will have length r sin θ . You can think of those lengths as the horizontal and vertical “components” of the hypotenuse. Notice in the above right triangle that we were given two pieces of information: one of the acute angles and the length of the hypotenuse. From this we determined the lengths of the other two sides, and the other acute angle is just the complement of the known acute angle. In general, a triangle has six parts: three sides and three angles. Solving a triangle means ±nding the unknown parts based on the known parts. In the case of a right triangle, one part is always known: one of the angles is 90 ◦ . Example 1.19

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